Blank for forming hollow polyhedrons.



A. H. WHEELER. BLANK FOR FORMING HOLLOW POLYHEADRO NS.

APPLICATION FILED MAR. 4. 19-18...

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ALBERT HARRY XVI-IEELER, OF WORCESTER, MASSACHUSETTS.

-BLANK FOB. FORMING HOLLOW POLYHEDRONS.

Specification of Letters Patent.

Patented Jan. 21, 1919.

, Application filed March 4, 1918. Serial No. 220.202.

To all whom z't may concern:

Be it known that I, ALBERT HARRY WHEELER, a citizen of the UnitedStates, residing at Worcester, in the county of WVorcester and State ofMassachusetts, have invented a new and useful Blank for FormingHollowPolyhedl-ons, of which the following is a specification.

This inveiition relates to the construction of polyhedrons of sheetmaterial in a simple and convenientway for the purpose of demonstratingprinciples of solid geometry in the Classroom and for similar purposes.

The principal objects of the invention are to provide a construction ofa blank from sheet material, as for example, paper which can 'bemanipulated in a certain way so as to produce a hollow polyhedron; toprovide constructions connected therewith for effectively holding theparts together at the angles, and of such a nature that no projectingparts come outside the hollow figure when it is completed, thusproducing a new article of manufacture in the polyhedron itself; and toprovide an improved hinge connection for pivotally joining two pieces ofsheet material so that the blank need not be formed of a single piece,but can be formed of several if desired. This construction is alsocapable of use independently of lthe production of polyhedrons. Furtherobjects and advantages of the invention will appear hereinafter.

Reference is to be had to the accompanying drawings, in which- Figure 1is a plan view of a blank shown in three pieces for forming a regulardodecahedron;

Fig. 2 is a plan of one end of said blank showing some of the adjacentfaces as secured in position to illustrate the manner in which the blankis manipulated to start to form the solid figure, the faces of the blanknot yet connected being broken away;

Fig. 3 is a view similar to Fig. 2 showing in direct plan a half of thefigure completed and the remainder of the faces also connected togetherto form the other half of the figure but being bent off to one side soas to give a view of the interior of the first mentioned half andshowingI the way in which the faces are held in position at Vthe angles;

Fig. 4 is a view of a complete dodecahedron in front elevation;

Fig. 5 is a view similar to Fig. 1 of a blank arranged for forming anirregular pol hedron formed of six square sides and eight triangularones;

Fig. 6 is a front elevation of the completed polyhedron which is inreality a cube with the six corners truncated in a regular manner;

Fig. 7 is a fragmentary view of a pair of faces or sheets showing amodified form of hinge, and

Fig. 8 is a. similar view showing another form.

In the form of the invention shown in the first four figures a blank isprovided consisting of three pieces A, B, C. Each one of these pieces,and in fact the entire blank is made up of a plurality of regularpolyo-ons, in this case pentagons, each one destined to constitute oneface of the dodecahedron shown in Fig. 4. It is to be understood thatthis blank can be all in one piece as shown in Fig. 5, but three piecesare illustrated here for convenience.

For the moment, ignoring the manner of connectino' these three piecesand assuming them to be all connected so that they act as a singlesheet, all the twelve faces of which are integral with each other andconstitute a continuous series, it will be seen that each of these facesis connected with the next one along a straight line which constitutesone of its edges. These connections are integral except in two places inthe form illustrated and they all constitute hinges about which thefaces 'can be bent with respect to each other. It will be seen also thateach of the faces is provided with either one or two projecting holdingor fastening tabs D.

It is to be observed that, each of the angles of the pentagon being onehundred and eight degrees, the several angles d, that is the obtuseangles formed between the adj acent edges of the polygon face and therespcctive tabs D are shown the same, that is one hundred and eightdegrees in order to foim a contact with the inside face of theV nextface. This gives a maximum holding force but it is to be understood thatthese' angles can be smaller so long as the distance between the two tipends of a tab is greater than the length of the corresponding edge ofthe polygon. The location of these several tabs is such that either theends of two 'edge of the base.

up in the same way against the other tabl D1, on face 1 and face '6 isbrought around tabs on one face or the end of one tab on one face and ofanother tab on the next face are located at the opposite ends of each ofthe hinged edges of the polvgon. p

I have numbered the several polygonsof this figure from 1 to 12inclusive, indicating the order in which they can be fold'ed-up althoughthe figure can be constructed in the reverse order. Face l can beconsidered as the base of the dodecahedron to be produced. Tn order toform the figure the face numbered 2 is turned un out of. the planeo'fcthe 'basel and brought of course'to the necessary angle which neednot be' stated o'rcalculated because the configuration of the parts issuch that it will not lockin position at any other angle. This is theonly thing necessary at that time. This havingbtfen accomplished theface numberedv 3 is bent about its hinge connecting it with face 2 tothe position in which it makes the same angle with the .base as' face 2.In doing this it will be observed that the 'tab D' on face 1 is broughtup inside face 3 and the location of this face, in the form shown, inposition with its lower edge contacting with the horizontal edge of thebase 1 causes this tab D' to hold the. above mentioned position with amaximum ofl efficiency. Now the tab D4 on the next face at the bottom,which just before the last inotion mentioned had to be folded back'against the inside of the face, can now be brought out into horizontalposition'on the base 1 and` the. face D4 swung around until its loweredge contacts with the third Now face 5- is brought and its tab D6 isalso brought into horizontal position and the faces are locked in thatplace by bringing the tab D2 inside of the face 6, sothat its lower edgewhich is now'horizontal projects over the tab D6' The and holds it inhorizontal position.

tab D4 holds the tabs D1 and D1 up in their` inclined positions againstthe inside surfaces of their respective faces 3 and 5, this tab D4 beinghorizontal and in contact with the base 1. The reason for making theangles alone hundred and eight 'degrees will:

now be apparent. The end edges of all the tabs D1, D1, D4 and D? fitagainst faces or tabs that at'their margins have to make thisV anglewith the adjacent faces in the form'show'n in Figs. 1 to 4;

These six faces are now 'in theposition' shown in'Fig. 3 in plan. vThatfigure is a little misleading because the otherhalf of the solid figureis not made usually independentlyl but the figure is made progressivelyall the way in accordance with the numbering on the faces. It isV shownmerely' in this way for illustrating where the faces and tabs arelocated when the figureis half done and it incidentally shows certainthings about the rest of the figure. It is true, however, that the'whole dodecahedron can be shown as constructed in that figure and thenthe parts united.

Now the face 7 is bent inwardly toward the center of the figure inordinary construction, and its tab D7 locked in between the two tabs D2and D2 and the rest of the figure is formed progressively as stateduntil the* last side numbered 12 is brought into position and there thelast tab D12 is tucled in behind the edge of thetab D,L0 at one end andthevtab D9 at theother to V,complete the figure. VVe 'get the'dodecahedronfas shown in Fig. 11 in which it 'will beseen 'that thereis no indication outside' that 'there isb any' fastenin'g means forholding the faces together', all the' tabs'beingby concealed inside.This is one of the objects of thei'inventiion and renders theresu'l'ting product 'a convenient one for use for demonstratingpurposes', but it'wi'll beseen that in'spite of the concealment of thefastening tabs they thoroughly fasten the parts ini position on accountof their Vangular relation to the faces and *iength 'I 4 I mightremark'at' this point that this identity 'in angles is not necessaryeven when the regular polyhedron is constructed and would have to bemodified inl 'casevof an ir-' regular polyh'edron. I have shownl the tabD12 as made of two pieces to facilitate'bending'it to complete thefigure. V

In the first four figures Il have shown the pieces A and C separatelyhinged to the piece B by a hinge construction. 'In' this case the hingeconstructionl consists simply of two hinge tabs E' extending'from eachof'the faces, each tab being shown as of a general rectangular form andhaving a space E' separating them. Immediatelynnder each tab E at onexedge there is a"slit e. These slits are for receiving thecorrespondingtabs on the other face.l :The distance from' the 4solid left endE'Iof'the right lhand tab E to the opposite'end of the left hand slot eadjacent to it 'on the face 10 `is'eouial to the length Vof the line bywhichT the' left hand tab E is connected with the' face 11,' and thesaine 'relationship is true of course for' the f other tabs. .'Thereforein'v` puttingf these tabs together when'the ytwo` faces lare placed backto back'they canbe slid together'l in the plane, being firstfolded'on'each `other until the back of th'eftab ,Eon the face 10substantially coincideswith the correspondt ing line,that is the line c'onithe tab on the face' 11.3' 'This requires fno 'bending .or distortionofthe faces yat'all. `Now?if'the'' two faces 10 and 11 are lfol'dedvup'on eachf other throughv any angle whatever, it will'. be found thatthese two'jedges'e' will slip) by each other and Vwe 'have athing'econnec-f out tearing or very badly distorting the parts unless the twofaces 10 and 11 are folded together in contact, in which case the twoedges e" can, if not naturally past each other, be brought past eachother and then the two parts slid by with a transverse sliding motion.ItV is to be 'noted that the angle between the line between the tab Eand the member 10, that is the line on which it is hinged, and the edgee' is reater than the one the hinge line makes with the edge of the slotE which happens in this case to be zero.A This shows up better in Fig. 7where the *latter angle is an acute one. This furnishes a stop toprevent lthe parts separating in all positions of the two sheets whichare hinged together except the one in which they are turned over intocontact with each other.l

' In Figs. 7 and 8 other forms of hinge are shown embo'dying the sameprinciples. In Fig. 7 these princ1ples are shown but in such form thatthe tabs F are without any slits but Vare 'simply made in the form of atrapezoid, in which the principles set forth above are carried out, theparts being assembled and taken apart in lthe same way as abovedescribed.

In Fig. 8 the tabs G are made in different form, but the relativedimensions and arrangements are the same as in Fig. 1, only the tabsinstead of being the same length are formed one long and the othershort, and they are shown as cut away near the center simply to avoidthe presence of surplus material.

In Figs. 5 and 6 the construction of 'an irregular polyhedron is shown,the faces of the same being made up of squares and triangles, and inthis case the tabs are shown provided with end angles of siXty degreesthe same as those of the triangular faces. This blank also is difierentfrom the one shown in the first four figures, because the parts are allone integral whole, but that is not a feature peculiar to this figure asthe same thing could be accomplished with the form shown in thosefigures. For that reason this construction will not be described indetail.

Although I have shown the invention as applied to one particular regularpolyhedron and one irregular one I am aware of the fact that it can beapplied to the construction of various regular and irregular polyhedronswithout change in principle, only such changes in the angles andrelations as are necessary to provide for different shapes.

Although I have illustrated and described only certain definite forms ofthe invention I am aware of the fact that modifications can be madetherein by any person skilled in the art without departing from thescope of the invention as expressed in the claims. Therefore I do notwish to be limited to the construction of any definite figure or to allthe details of construction, but what I do claim is 1. A blank of sheetmaterial for use in constructing a hollow polyhedron, said blank beingshaped to provide the number of polygonal faces necessary to produce thedesired shape, said faces being flexibly connected with each other in acontinuous series, the line of connection in each case being along oneof the edges of the face, said faces having flexibly connected tabsextending beyond the boundaries of the respective polygons at the endsof said lines of connection to hold the faces together.

2. A blank for use in producing a polyhedron made up of a number ofpolygonal faces, each connected to another one along an edge by aflexible connection constituting a hinge, and a projecting hinged tab ateach end of the hinge, each tab being adapted to fit against the surfaceof an adjacent face when the figure is completed to hold the faces inposition.

3. A blank of sheet material for use in constructing a hollow polyhedronshaped to provide the number of regular polygonal faces necessary toproduce the desired shape, said faces being flexibly and integrallyconnected with each other in a continuous integral series along theedges of the faces, and tabs flexibly connected with the several facesand having ends extending beyond the ends of the faces for the purposeof folding inside the adjacent faces and holding them in position.

4. A blank of'sheet material for use in constructing a hollow polyhedroncomprising the number of polygonal faces necessary to produce thedesired shape, said faces being flexibly connected with each other, saidfaces having flexibly connected tabs extending beyond the boundaries ofthe respective polygons at the ends of the lines of connection, certainof said tabs having their ends projecting beyond the line with whichthey are connected to the face so as to fold in behind an adjacent face.

5. A blank for use in producing a polyhedron made up of a number ofpolygonal faces, each connected to another one along an edge by aflexible connection constituting a hinge, one or both of each twoadjacent faces having a projecting hinged tab at the end of the hingeadapted to fold behind the inner surface of an adjacent face when thefigure is completed, to help hold the faces in position, one of saidtabs having its ends forming projections located a distance apartgreater than the length of the hinge line at the edge thereof by whichsaid tab is connected with the adjacent faces.

6. A blank of sheet material for use in eonstructing a hollowpolyhedron, shaped to provide the number of polygonal faces necessary toproduce the desired, shape, said faces being flexibly connected withVeach other and having fl'exibly: connected tabs ei;- tending beyond theboundaries of. the respective polygons at thefiends' of'the` lines ofvconnection,one of said faces being 'sepa'f i'ably 'connected withanother and adapted to swing about. the 'separable'connection as a,

'1 in 'f' ,it V

` 7. A blank for use in producing av polyhedron madeup ofial number of'`polygonal faces, each connected to *"'anothe'r one; along an 'edge by 'aflexible 'connection`-constitlitiiig a hin'ge; said' hinfge'compris'i'ng'g':twoftabsb eXfj tending from each' face,' saidtabsfbe'in'g sep',-v arated from each other'and 'having'ia'space for'the reception of a tab on the otherxface, means 'Wherebyi the' 'two'faeS. when in Vconf tact fwith each other can be `moved .togetlflelI bya' Vmotion in aV plane until the rear lends of the respective tabs comeinto contact and pass each other and then the twoV faces will behingedly vco'nnlebzcted with each: other,` one or both of each'itwovadjacent,faces having a projecting hinged tab, atfthe `end of the hingeadapted to fit against I theI siirfa'ce of an adjacent face vwhenV vthe`figure is comf pleted to help hold the faces in position,"

8. lA body of sheet `material co'mpri's'ing two members or faceseachfpoflthem having two tabs projecting therefromjin the planethereof,b the space between "the ,two tabsfjon each one, along thestraight ,boundary line between the vmember and :the tabs, being equalto the' lengthV of a tabonfthe other piece so that the two members canbe united by placing them in contact and moving them together with the'forwardedge Aof each `rtab guide'd'behind the adjacent edgefof thecorrespondingtab onthe other member until the rear edge of ,the forwardtab on'each member coincides with the rear edge of the tab'on' the othermember and whereby the' two'lmembelfjli'e fihlls hinged 'together and'readily) Separebla Without,1hex1di1ie=r-whenfin,

that., one position.

"10. AT hollQw. pelyhedmn closetV @a all sides formedjdf .sheetfmateriall'andr provided With fatening meanslocated;elitirelyiinside it', atrthe:ends .ofgsornefofrits edgesffand con'.-V sti-tebingV Coatinuatipns fatthe anda- 1f:-S0nf1e.A

11. As,r articlewrof: mannfacture; a l body comprising two parts,formed'of, sheet lInfa-` tei'ial, having av hinge', connectionyybetweenthem comprising. Itwo tabs ,ony eacnhnone,v the body of .eachtabbeinglongenthanfthe6 neck.

which3 joins, vit vto V,themaiii partof :the sheetmaterialfsaidtabsfionflach Part. fbeing :Spacedf apart to Vpermit the t.entrance between I them.

of aftab On'th/Otheripart.

As .article of manufacture,, aL body compris'ing two parts, formed ofsheet l:material', having a ,y b hingei connection I. between them'comprisingutwo, spaced Ytabsxon each, thev .body of, each. tab being;longerthanfthe neckwhichfjoins it .tothe .mainfpart :of the Y sheetLmatferial'yt the correspondingiedges vof,

saiditabsj being yparallel and foneof each' having an `edge.,,crossing aj correspondingy edge on a tab of the other part andlocated at, ananglezto the ,outerr zedges of the sheet and constituting ,,a stop, `.toprevent; theiry separation, exceptxwhen theutwo, partsv are folded backf into contact. fwith beachb other.`

Invtestimony whereof I :have hereunto aflixped my signature.

ALBERT [HeamnwHEELER-fifl Copies of this patent may leep obtained for`fivex cents each, by gddressing themf'CommissipneggofAgatents,`

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